INHIBITORY EFFICIENCY AND PHYSICOCHEMICAL PROPERTIES OF LIPIDS FROM LEAVES AND JUICE OF ALOE ARBORESCENS Mill.

The composition of lipids isolated from leaves and juice of A. arborescens (7 years ago) and the inhibitory efficiency of lipids from leaves of A. arborescens were studied. The phospholipid (PL) fractions were divided by means of TLC method. The quantitative proportion of PL fractions was determined by spectrophotometrically. The more substantial differences in the composition of PL from leaves and juice of A. arcorescens are revealed in the proportion of the more poorly oxidizable fractions of PL. The more low relative content of PL in the total lipid composition from leaves compared with than in lipids from juice, and shares of sterols are the same for lipids from leaves and juice cause 16% diminution of the molar ratio of [sterols]/[PL] in lipids from juice of A. arborescens. Lipids from leaves are known to characterize the high inhibitory efficiency that is demonstrated by model of the low temperature autoxidation of methyl oleate in the thin layer. Using UV-spectroscopy and the mathematic analysis of spectra by Gauss method the presence of the biologically active substances which contain in lipids was analysed. There are only flavonoids in the chloroform solution of lipids from juice and flavonoids and carotenoids in the small quantity in the chloroform solution of lipids from the leaves of A. arborescens.

Convergence for the optimal control problems using collocation at Legendre-Gauss points

The convergence of the novel Legendre-Gauss method is established for solving a continuous optimal control problem using collocation at Legendre-Gauss points. The method allows for changes in the number of Legendre-Gauss points to meet the error tolerance. The continuous optimal control problem is first discretized into a nonlinear programming problem at Gauss collocations by the Legendre-Gauss method. Subsequently, we prove the convergence of the Legendre-Gauss algorithm under the assumption that the continuous optimal control problem has a smooth solution. Compared with those of the shooting method, the single step method, and the general pseudospectral method, the numerical example shows that the Legendre-Gauss method has higher computational efficiency and accuracy in solving the optimal control problem.

Novel Symmetric Numerical Methods for Solving Symmetric Mathematical Problems

The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equations is conducted with the help of numerical integration theory. It is commonly known that a class of problems can be solved by applying numerical integration. The construction of the quadrature formula has a direct relation with the computation of definite integrals. The theory of definite integrals is used in geometry, physics, mechanics and in other related subjects of science. In this work, the existence and uniqueness of the solution of above-mentioned equations are investigated. By this way, the domain has been defined in which the solution of these problems is equivalent. All proposed four problems can be solved using one and the same methods. We define some domains in which the solution of one of these problems is also the solution of the other problems. Some stable methods with the degree p<=8 are constructed to solve some problems, and obtained results are compared with other known methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. In addition, symmetric methods are constructed for comparing them with other well-known methods in some symmetric and asymmetric mathematical problems. Some of our constructed methods are compared with Gauss methods. On the intersection of multistep and hybrid methods have been constructed multistep methods and have been proved that these methods are more exact than others. And also has been shown that, hybrid methods constructed here are more exact than Gauss methods. Noted that constructed here hybrid methods preserves the properties of the Gauss method.

TRANSFORMATION OF INTERNAL ORGANIZATIONAL RATING OF LABOR IN THE CONDITIONS OF DIGITALIZATION

The article is devoted to topical problems of labor rationing in organizations of the real sector of the economy. First, the author reveals the meaning and essence of labor rationing, gives a retrospective of approaches to labor rationing, clarifies the concept and content of intra-organizational labor rationing in modern conditions. Taking into account the possibilities of using modern information and communication technologies in the organization of labor rationing, due attention is not paid. In this regard, the leading organizations of various types of activities of the Altai Territory studied the features and modern problems of intra-organizational regulation of labor. The provision of the staff and the conditions for training specialists — work rate setters in organizations, the used normative reference books, the applied methods of work rate setting, assessed the quality level of the current labor standards. The author has systematized traditional and modern domestic and foreign methods of microelement rationing of labor. Based on the results of the study, the author presents specific recommendations for building a microelement regulatory framework for an organization in the context of digitalization. Among them deserve the greatest interest, according to the author, specific automated systems and programs for the rationing of labor, as well as the graphic-analytical method and the Gauss method.

Solving Systems of Linear Algebraic Equations with the Use of an Selective Regularization

The solution of systems of linear algebraic equations, which matrices can be poorly conditioned or singular is considered. As a solution method, the original matrix is decomposed into triangular components by Gauss or Chole-sky with an additional operation, which consists in increasing the small or zero diagonal terms of triangular matrices during the decomposition process. In the first case, the scalar products calculated during decomposition are divided into two positive numbers such that the first is greater than the second, and their sum is equal to the original one. In further operations, the first number replaces the scalar product, as a result of which the value of the diagonal term increases, and the second number is stored and used after the decomposition process is completed to correct the result of calculations. This operation increases the diagonal elements of triangular matrices and prevents the appearance of very small numbers in the Gauss method and a negative root expression in the Cholesky method. If the matrix is singular, then the calculated diagonal element is zero, and an arbitrary positive number is added to it. This allows you to complete the decomposition process and calculate the pseudo-inverse matrix using the Greville method. The results of computational experiments are presented.

Dynamic Vibration Extinguished on a Viscously Elastic Base

The aim of the work is to develop algorithms and a set of programs for studying the dynamic characteristics of viscoelastic thin plates on a deformable base on which it is installed with several dynamic dampers. The theory of thin plates is used to obtain the equation of motion for the plate. The relationship between the efforts and the stirred plate obeys in the hereditary Boltzmann Voltaire integral. With this, a system of integro-differential equations is obtained which is solved by the method of complex amplitudes. As a result, a transcendental algebraic equation was obtained to determine the resonance frequencies, which is solved numerically by the Muller method. To determine the displacement of the point of the plate with periodic oscillations of the base of the plate, a linear inhomogeneous algebraic equation was obtained, which is solved by the Gauss method. The amplitude - frequency response of the midpoint of the plate is constructed with and without regard to the viscosity of the deformed element. The dependence of the stiffness of a deformed element on the frequency of external action is obtained to ensure optimal damping of vibrational vibrations of the plate.

Vibrations of Cylindrical Shell Structures Filled With Layered Viscoelastic Material

A thin-walled shell and a thick-walled mass (cylinder) in contact with it, made of a different material, are structural elements of many machines, apparatus, and structures. The paper considers forced steady-state vibrations of cylindrical shell structures filled with a layered viscoelastic material. The study aims to determine the damping properties of vibrations of a structurally inhomogeneous cylindrical mechanical system under the influence of harmonic loads. The dynamic stress-strain state of a three-layer cylindrical shell filled with a viscoelastic material under the action of internal time-harmonic pressure is investigated. The oscillatory processes of the filler and the bonded shell satisfy the Lamé equations. At the contact between the shell and the filler, the rigid contact conditions are satisfied. Dependences between stresses and strains for a linear viscoelastic material are presented in the form of the Boltzmann-Voltaire integral. The method of separation of variables, the method of the theory of potential functions (special functions), and the Gauss method are used to solve this problem. Based on the analysis of the numerical results, it was found that the dependence of the resonant amplitude of the shell displacements on the viscous properties of the filler is 12-15%. Analysis of the results obtained shows that the study of vibrations of shells containing fillers according to the rod theory will lead to rather large erroneous results (up to 20%).

A new approach to determining the constructive balance for the design of customised patterns of men garments

The objective of this study was to develop a new method of designing ergonomically shaped men’s jackets that perfectly adapt to the customer’s body shape and style (i.e. custom made jackets). The study included 10 adult subjects who prefer to wear formal jackets to work. These subjects underwent 3D scans, and the images were used to execute the study objective. The constructive balance values of men’s jacket patterns were determined by considering the characteristics of the subject’s torso and preferred style. The longitudinal contours of the torso were described by parabolic equations, which were solved with the Gauss method. The obtained value of the constructive balance (1.5 ÷ 3 cm) was used to design jackets using a particular module of Gemini CADs, which allows the mathematical relations between the positions of specific points on the contour of a men’s jacket to be expressed. The pieces are designed in Gemini’s geometric layer. The designer can establish the mathematical relations based on his/her pattern-making competencies and human body and garment evaluation results. In a 3D virtual environment (Lectra-Modaris 3D), the customer’s avatars were dressed with the same jacket model but with different bust lines and various widths on the lateral side. The bust line level was established by using the backside length (measured from the seven-vertebra until the armpit level) and an allowance value, which was established after the human body backside curvature, garment silhouette, number of layers, etc. were analysed. Two variants of the jacket model were designed: a regular- and a medium-fit at the bust level (the value of the constructive bust allowance was 7 ÷ 10 cm). The garment position on the body was evaluated by studying its relative displacement when the avatar performed regular movements (moving his upper limbs). Thirteen cases were considered significant and used to analyse the jacket hemline relative displacement (relative to its horizontal position). These cases were analysed with factorial programming and a rotatable compound central programme with two independent variables. The best shape, size and position of the jacket on the virtual body were determined for the following situation: the value of the backside allowance (longitudinal direction) was between 1.6 and 4 cm, and the width of the jacket on the lateral side was calculated with the percentage of the constructive bust allowance ranging from 49% to 51%. With these parameters, the garment appears to fit the body well.

Dynamic Stress-Deformed States of a Circular Tunnel of Small Position Under Harmonic Disturbances

There are many underground tunnels of various shapes located in seismically active areas that need to be protected from seismic impacts. The paper considers the impact of harmonic waves on a cylindrical shell located in a viscoelastic half-plane. The study's main purpose is to determine the stress-strain state of a cylindrical shell when exposed to harmonic waves. The basic equation of viscoelasticity in displacements with the corresponding boundary conditions is obtained. The problem posed is solved in mixed potentials that satisfy the wave equation with complex parameters. The solution is expressed in terms of special Bessel and Hankel functions. As a result of multiple reflections, a system of algebraic equations with complex coefficients is obtained. In the future, this system is solved by the Gauss method with the selection of the main element. The analytical solution is obtained in infinite series, the convergence of which is investigated numerically. The numerical results were obtained using the MATLAB software package. The reliability of the research results is confirmed by good agreement with theoretical and experimental results and those obtained by other authors.

Comparison of methods for solving systems of linear equations occurring in tasks with a changing configuration of the contact surface

The article discusses iterative algorithms for solving systems of linear algebraic equations arising when solving problems of contact interaction of thermoelastic bodies with a changing configuration of the contact surface. The implementations of the modified symmetric successive upper relaxation method (MSSOR), modified successive upper relaxation method (MSOR), modified Jacobi method (MJOR) and Uzawa method as well as algorithms based on the Gauss method with two options for iterative refinement, allowing to consider the exit from the contact of the contact border sections, are presented. The results of the application of these algorithms to the demo problem that simulates thermomechanical processes in the section of the fuel element, which includes two tablets and a fragment of the shell, are presented.